Rinse the pork roast, and pat it dry with paper towels. Heat the olive oil in a large pot.
Place the pork roast in the pot and cook each side 6 to 8 minutes, or until the pork is golden brown. Searing the meat helps to give it flavor. Once the pork roast is golden brown, remove the pot from heat and set it aside.
Add barbecue sauce, tomato sauce, chicken stock, chili powder, smoked paprika, garlic powder, onion powder, salt, Worcestershire sauce, mustard, apple cider vinegar, and brown sugar to a mixing bowl. Whisk to combine the ingredients to make a pulled pork sauce to season the meat.
Coat the inside of a large slow cooker pot with nonstick cooking spray. Place the chopped onion and bell peppers in the bottom of the slow cooker pot.
Carefully place the browned pork roast into the slow cooker pot. Pour the pulled pork sauce over the pork.
Close the slow cooker lid. Cook the pork roast and other ingredients on LOW heat setting for about 8 to 10 hours or on HIGH heat setting for 5 to 6 hours, or until the pork reaches an internal temperature of 200 degrees Fahrenheit as measured by an instant read meat thermometer placed at the thickest part of the meat.
The slow cooked pork roast should be pull apart tender and easy to shred once it’s done. Use two forks to shred the pork, or allow the pork to cool, remove it from the pot (carefully, as the pork will be tender and ready to fall apart), and cut the pork into chunks to serve.
To make pulled pork sliders or sandwiches, layer the meat between two sandwich buns or dinner roll halves to make each pulled pork sandwich or slider. Serve slow cooker pulled pork sliders or sandwiches with your favorite pulled pork toppings.